一种改进的k_means聚类算法_英文_夏士雄

Abstract : In allu sion to the d isadvan tage of hav in g to ob tain the num ber of clu sters of data sets in advance and the sen sitiv ity to selecting in itial clustering cen ters in the k-m ean s algo rithm, an i m p roved k-m ean s clustering algorithm is propo sed. F irs, t the con cep t of a silhouette coeff icien t is in troduced, and the op ti m al clustering num berK op t of a data set w ith unknown class in fo r m ation is conf ir m ed by calcu lating the silhouette coef ficien t o f ob jects in clusters under d ifferen t K values . T hen the d istribution of the data set is ob tained th rough h ierarch ical clustering and the in itial clusterin g -cen ters are con fir m ed. F inally , the clustering is comp leted by the trad itional k-m eans c lu stering. By the theoretical analysis , it is p roved that the i m proved k-m ean s clustering algorithm has p roper com putational com p lexity. The experi m en tal resu lts o f IR IS testing data set show that the algorithm can d istingu ish d ifferen t clu sters reasonab ly and recogn ize the outliers eff icien tly , and th e en tropy generated by th e a lgorithm is low er . K ey words : clustering ; k-m ean s algo rithm; silhouette coeff icien t
Received 2007 -05 -18 . F oundation item s : The N ational N atural Science Foundation o f C hina ( N o. 50674086), Specialized R esearch Fund for theD octora l Program o f H igher Education ( N o. 20060290508 ), the Y ou th S cien tif ic R esearch Foundation of C h ina U niversity of M in ing and Techno logy ( N o. 2006A 047). B iography : X ia Sh ix iong( 1961) ), m ale, p rofessor , xiasx@ cum .t edu . cn .
A s an i m po rtant re search branch o f da ta m ining, cluster analy sis a i m s to d iv ide data ob je cts in to groups based on the ir attributes and relations . And th e ob jects have h ig h si m ilarity to one ano th er w ithin the sam e groups and have high d issi m ila rity to th e objects in [ 1] o th er g ro ups . T he m o st w ell know n and comm only used c lu ste rin g algorithm s are k-m eans , k-m edo ids and the ir varia t io ns . The com putationa l com plex ity of th e k-m eans al gorithm is low and the k-m eans a lg o rithm m ay only [ 2] f ind lo ca l opti mu m rather than th e g lo bal . C onsid er ing th e inna te li m itat io n o f the k-m eans m eth od , th is paper propo ses an i m proved k-m eansm ethod . T he i mproved m ethod can no t only effectiv ely dec ide appropriate nu m ber o f clusters , but also properly se le ct in itial po in ts fo r k-m eans . In add ition , the i m proved k-m eans algo rith m has good clustering results .
ei = w here p ij =
Ep
j= 1
L
ij
log2 p ij
( 1)
1 C riteria of C lustering
111 Entropy Entropy depicts the dispersa l of objects belong ing to the sam e class be in g m erged in to dif ferent clusters . A ccording to the distribution o f c la sses , w e can calcu [ 3] late th e entropy of each c lu ster by
Jou rna l of Southeast U n iversity ( Eng lish Ed ition)
V o.l 23, N o. 3, pp. 435 -IS SN 1003) 7985
I m proved k-m eans clustering algorithm
xI C i
E
dist(x, ci )
436
X ia Sh ix iong, L iW enchao , Zhou Yong, Zhang Le,i and N iu Q iang w If th e object is already m erged intoK op t c lu sters l in step ⑨, then this object rem a in s in the o rig ina l clus ter . x E lse ca lculate th e distances betw een th is object l and the centro id s o f ex isting K clusters . y If the distances exceed the th resho ld set by the l user , then th is object is considered as an outlier . z E lse m erge th is object into the cluster w ith the l clo sest distance and upda te th e centro id of th e c lu ster . { Until no ob ject changes in the w ho le data se. l t T he i m pro ved k-m eans clustering algorith m refers to t w o param eters : REAR andE p s. If w e directly obta in K op t clusters in step ⑤, th isw ill cause severa l centro id s o f clusters to be scattered , so w e ter m inate hierarchica l clusterin g until rem ain in g K op t + REAR clusters . T he va lue of REAR is set acco rdin g to the percentage o f hi erarchical clustering. T he goal of th resho ld E p s is to reco gn ize few outlie rs in the data set accurate ly. 21 2 Analy sis o f com putationa l com plex ity o f algo rithm The i m pro vedk-m eans clustering a lgorithm can be partit io ned in to three phases : S tep ① f inds the opti mal num ber of c lu stersK op t; steps ② to ⑨ adopt the ag g lom erate algorithm to produce initial in for m ation fo r k-m eans ; steps ⑩ to { adopt k-m eans to accom plish a l cluster . In the f irst phase, w e need to ca lculate th e sil houe tte coeff icient repeated ly to obtain K op t. So the com putatio nal com p le x ity o f this step is O ( I @ n ), w here I represents the ti m es o f calculating the silh ou [5]